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Strongly Goldie Dimension | | Liang Shen
; Jianlong Chen
; | | Date: |
9 Oct 2005 | | Abstract: | Let $R$ be an associative ring with identity. A unital right $R$-module $M$ is called strongly finite dimensional if Sup${{
m G.dim} (M/N) | Nleq M< +infty$. Properties of strongly finite dimensional modules are explored. It is also proved that: (1)If $R$ is left $F$-injective and strongly right finite dimensional, then $R$ is left finite dimensional. (2) If $R$ is right $F$-injective, then $R$ is right finite dimensional if and only if $R$ is semilocal. Thus the Faith-Menal conjecture is true if $R$ is strongly right finite dimensional. Some known results are obtained as corollaries. | | Source: | arXiv, math.RA/0510175 | | Other source: | [GID 762423] math/0510175 | | Services: | Forum | Review | PDF | Favorites | |
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